These people aren't talking about sports that require skill. They just mean physical activity anyone can do, like hiking.

The actual meaning of the advice is to find a physical activity you can tolerate in order to find a mate who isn't fat. It is a way to make their completely reasonable and relatable position on fat people seem like something noble. "My mate and I enjoy hiking. It is our shared interest." The reason I know what I'm saying is true is because every time this discussion comes up, people peddle the shared interest bullshit and inevitably bring up 'physical activity.' And sorry for getting a hair up my ass about it, I just find it crazy when people can't just say what they mean: If you are an average man who prefers a woman with a nice body and you dislike or are unsuccessful on dating apps, try going to a group activity that will filter out fat chicks. The end. Nothing pretending this is anything but another attempt at finding a mate.

You're getting hung up on "fat" here as if it's purely an aesthetic preference

Physical activity filters for people who actually care about themselves. If you can't be bothered to look after your body, then you're likely not going to be any good at looking after your relationship, your family, raising children etc.

That is such a good way of putting it and I agree wholeheartedly. The body and mind are like the absolute foundation that you build other things on top of. If your mind and body are not sound, then what chance do the other things have?

I kind of disagree with this connection that fat women == not going to be any good at relationship and family and children. In my experience fatness has no correlation with their ability to raise kids or their attentiveness in a relationship (just go to an average parent meeting at an average school). Often times it’s actually the opposite because they can be more understanding as you both get old and unattractive together, or are more likely to work harder at it because they know they’re at a disadvantage for their fatness.

Of course I also know plenty of guys who cheat on their wife as she gets older and less hot (the classic “he gets older but all his dates are the same age”), and theres a danger for thin women who are filtered for their physical traits like this.